Abstract
In this paper, we prove sharp isoperimetric inequalities for lower order eigenvalues of Neumann Laplacian on bounded domains in both compact and noncompact rank-1 symmetric spaces. Our results generalize the work of Wang and Xia for bounded domains in the hyperbolic space (Xia and Wang in Math Ann 385(1–2):863–879, 2023), and Szegö–Weinberger inequalities in rank-1 symmetric spaces obtained by Aithal and Santhanam (Trans Am Math Soc 348(10):3955–3965, 1996).
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Communicated by R.M. Schoen.
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The research of the second author is supported by Natural Science Foundation of Jiangsu Province Grant No. BK20231309.
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Meng, Y., Wang, K. Isoperimetric inequalities for Neumann eigenvalues on bounded domains in rank-1 symmetric spaces. Calc. Var. 63, 113 (2024). https://doi.org/10.1007/s00526-024-02726-4
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DOI: https://doi.org/10.1007/s00526-024-02726-4